LCM of fractions with coprime denominators: Compute the LCM of 2/3, 3/5, 4/7, and 9/13 using the LCM(numerators)/GCD(denominators) rule.

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:For fractions, LCM = LCM of numerators divided by GCD of denominators. When denominators are pairwise coprime overall (GCD = 1), the LCM simplifies to just the LCM of numerators as an integer. Given Data / Assumptions: Fractions: 2/3, 3/5, 4/7, 9/13. All denominators 3, 5, 7, 13 are pairwise coprime, so overall GCD is 1. Concept / Approach:Compute LCM of numerators 2, 3, 4, 9. Then divide by GCD of denominators (which is 1), meaning the LCM is simply that numerator LCM. Step-by-Step Solution: LCM(2, 3, 4, 9) = 36 (since 4 contributes 2^2 and 9 contributes 3^2).GCD(3, 5, 7, 13) = 1.LCM of the fractions = 36 / 1 = 36. Verification / Alternative check: Check divisibility: (36) ÷ (2/3) = 54; ÷ (3/5) = 60; ÷ (4/7) = 63; ÷ (9/13) = 52; all integers. Why Other Options Are Wrong: 1/36 and 1/1365 are reciprocals-like values, not suitable here. 12/455 does not produce integer quotients with all given fractions. Common Pitfalls: Treating the LCM of denominators instead of their GCD for the fraction-LCM formula. Final Answer: 36

LCM of fractions with coprime denominators: Compute the LCM of 2/3, 3/5, 4/7, and 9/13 using the LCM(numerators)/GCD(denominators) rule.

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